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Recent research in mice indicates that luminance-independent fluctuations in pupil size predict variability in spontaneous and evoked activity of single neurons in auditory and visual cortex. These findings suggest that pupil is an indicator of large-scale changes in arousal state that affect sensory processing. However, it is not known whether pupil-related state also influences the selectivity of auditory neurons. We recorded pupil size and single-unit spiking activity in the primary auditory cortex (A1) of nonanesthetized male and female ferrets during presentation of natural vocalizations and tone stimuli that allow measurement of frequency and level tuning. Neurons showed a systematic increase in both spontaneous and sound-evoked activity when pupil was large, as well as desynchronization and a decrease in trial-to-trial variability. Relationships between pupil size and firing rate were nonmonotonic in some cells. In most neurons, several measurements of tuning, including acoustic threshold, spectral bandwidth, and best frequency, remained stable across large changes in pupil size. Across the population, however, there was a small but significant decrease in acoustic threshold when pupil was dilated. In some recordings, we observed rapid, saccade-like eye movements during sustained pupil constriction, which may indicate sleep. Including the presence of this state as a separate variable in a regression model of neural variability accounted for some, but not all, of the variability and nonmonotonicity associated with changes in pupil size. NEW & NOTEWORTHY Cortical neurons vary in their response to repeated stimuli, and some portion of the variability is due to fluctuations in network state. By simultaneously recording pupil and single-neuron activity in auditory cortex of ferrets, we provide new evidence that network state affects the excitability of auditory neurons, but not sensory selectivity. In addition, we report the occurrence of possible sleep states, adding to evidence that pupil provides an index of both sleep and physiological arousal.